Question

1) Find f(g(x)) and9(f(c)).Given: f(x) = 5x; g(x) = x - 3f(g(x))

Answer 1

Given the following:

f(x) = 5x

g(x) = x - 3

A.) Let's determine f(g(x)):

This means that we will be using the function of g(x) = x - 3 as the x in the f(x) = 5x.

We get,

`\text{ f(g(x)) = 5x }\rightarrow\text{ f(x-3) = 5(x - 3)}`
`\text{ f(x -3) = 5x - 15}`
`\text{ f(g(x)) }=\text{ f(x - 3) = 5x - 15}`

A.) Let's determine g(f(x)):

This means that we will be using the function of f(x) = 5x as the x in the g(x) = x - 3 .

We get,

`\text{ g(f(x)) = x - 3 }\rightarrow\text{ g(5x) = (5x) - 3}`
`\text{ g(f(x)) = g(5x) = 5x - 3}`